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We develop U(1) slave spin-rotor theory, suggesting a metal-metal transitionfrom Landau's Fermi-liquid state to a bad metal phase, as U(1) slavecharge-rotor theory [Phys. Rev. B {\bf 70}, 035114 (2004)] describes ametal-insulator transition from Landau's Fermi-liquid state to a spin-liquidphase. U(1) slave spin-rotor formulation allows us to generalizeHertz-Moriya-Millis theory for ferromagnetic quantum phase transitions,replacing Landau's Fermi-liquid state with an incoherent metallic phase. As aresult, we argue that localized magnetic moments emerge to govern quantumcritical physics in bad metals.

Critical field theory for ferromagnetic quantum criticality in the strong coupling regime of Hertz-Moriya-Millis theory